A model of heat conduction

We construct a model of a chain of atoms coupled at its ends to two reservoirs at different temperatures. In a weak coupling limit the atoms obey a stochastic evolution law and have an equilibrium state with a uniform temperature gradient along the chain.     

Simple one-dimensional model of heat conduction which obeys Fourier's law.

We present the computer simulation results of a chain of hard-point particles with alternating masses interacting on its extremes with two thermal baths at different temperatures. We found that the system obeys Fourier's law at the thermodynamic limit. This result is against the actual belief that one-dimensional systems with momentum conservative dynamics and nonzero pressure have infinite thermal conductivity. It seems that thermal resistivity occurs in our system due to a cooperative behavior in which light particles tend to absorb much more energy than the heavier ones.     

基于热质运动概念的普适导热定律

根据爱因斯坦的质能等效关系式,热能具有的等效质量称为热质,从而在固态和气态介质中分别建立了声子气质量和热子气质量的概念.应用牛顿定律建立了含有驱动力、阻力和惯性力的热质(声子气或热子气)运动的动量守恒方程.由于热量在介质中的传递本质上就是热质(声子气和热子气)在介质中的运动,所以热质动量守恒方程就是普适的导热定律,能够统一描述各种条件下的导热规律.当热流密度不是很大从而热质惯性力可以忽略时,热质动量守恒方程就退化为傅里叶导热定律,这表明傅里叶导热定律是特殊条件下的导热定律,对于微纳尺度条件下的导热,热流密度可以极高,由速度空间变化引起的惯性力不能忽略,在稳态导热情况下也将出现非傅里叶导热,此时在计算或者实验中不能用热流密度除温度梯度求导热系数.在超快速加热条件下,必需考虑惯性力,与基于CV导热模型的波动方程相比,普适的导热定律增加了因速度空间变化引起的惯性力项,所以在介质中热波叠加时不会出现产生负温度的非物理现象,表明基于热质运动概念的普适导热定律更为合理. 关键词： 傅里叶导热定律 普适导热定律 热质运动 非傅里叶导热     

Beyond the Fourier heat conduction law and the thermal no-slip boundary condition

The problem of heat slip flow along solid walls is investigated within the framework of modern thermodynamics. The underlying idea is to elevate the heat flux at the boundary to the status of independent variable. General boundary conditions are obtained from the constraint imposed by the second law of thermodynamics expressing that the rate of entropy production is non-negative. In parallel, evolution equations for the heat flux inside the bulk of the system are also formulated.     

Gas-kinetic model of heat conduction of heterogeneous substances

A theoretical approach is proposed for calculating thermal conductivity κ of an arbitrary type of porous structures as a function of porosity ξ, temperature T, density ρ, and a number of other parameters. The general computational algorithm is based on the theory of nonequilibrium processes. Its modification in the language of gas-kinetic approximation makes it possible to derive compact relations for κ and to easily estimate the corresponding dependences. Theoretical formulas are compared to experimental results and their good agreement is demonstrated for a specific example of refractory concrete, which is a very important substance for practical applications.     

Charge-exchange transitions on neighbouring nuclei in a semi-microscopic model

The (p, n) scattering from a target of a core plus one nucleon (or hole) to the isobaric analogue and anti-analogue state is described in terms of the Lane potential of the core and a local effective interaction between the projectile and the excess particle (or hole). In this model it is possible to distinguish static shell fluctuations from certain changes in the reaction dynamics between proximate nuclei. In particular, it is suggested that the giant resonance effects in (p, n) depend strongly on the target nucleus.     

On the entropy production for the Davies model of heat conduction

The formula for the entropy production in open quantum systems is examined for the Davies model of heat conduction.This work is supported by Polish Ministry of Higher Education Science and Technology, project MRI 7.     

A systematic semi-microscopic analysis of the scattering of oxygen isotopes

A semi-microscopic theory for the scattering of nuclei near closed shells is discussed in detail and applied to the bulk of the presently available experimental data. The results generally indicate that the single-folding model can be used to extrapolate the effective interactions for heavy-ion scattering away from closed-shell systems. We particularly discuss the importance of the imaginary part of the valence interaction and the effects of higher-order reorientation and two-step transfer processes.     

The stationary state and the heat equation for a variant of Davies' model of heat conduction

We study a variant of Davies' model of heat conduction, consisting of a chain of (classical or quantum) harmonic oscillators, whose ends are coupled to thermal reservoirs at different temperatures, and where neighboring oscillators interact via intermediate reservoirs. In the weak coupling limit, we show that a unique stationary state exists, and that a discretized heat equation holds. We give an explicit expression of the stationary state in the case of two classical oscillators. The heat equation is obtained in the hydrodynamic limit, and it is proved that it completely describes the macroscopic behavior of the model.     

A constrained variational principle for heat conduction

The heat equation is re-studied in this Letter in view of variational theory. By the semi-inverse method, a variational principle for the heat conduction is obtained, which is first appeared in the literature. The physical understanding of the obtained variational principle still needs further explanation.     

A meshless model for transient heat conduction analyses of 3D axisymmetric functionally graded solids

A meshless numerical model is developed for analyzing transient heat conductions in three-dimensional （3D） axisymmetric continuously nonhomogeneous functionally graded materials （FGMs）. Axial symmetry of geometry and boundary conditions reduces the original 3D initial-boundary value problem into a two-dimensional （2D） problem. Local weak forms are derived for small polygonal sub-domains which surround nodal points distributed over the cross section. In order to simplify the treatment of the essential boundary conditions, spatial variations of the temperature and heat flux at discrete time instants are interpolated by the natural neighbor interpolation. Moreover, the using of three-node triangular finite element method （FEM） shape functions as test functions reduces the orders of integrands involved in domain integrals. The semi-discrete heat conduction equation is solved numerically with the traditional two-point difference technique in the time domain. Two numerical examples are investigated and excellent results are obtained, demonstrating the potential application of the proposed approach.     

Novel heat conduction model for bridging different space and time scales

This exposition describes a novel heat transport model and an underlying unified theory emanating from the physics of the Boltzmann transport equation which acknowledges simultaneously the coexistence of that termed as slow processes (at low energies) and fast processes (at high energies) as heat carriers while describing the evolution of heat transport characteristics spanning both spatial scales (characterizing ballistic to diffusive limits), and also time scales (characterizing finite to infinite heat propagation speeds).     

A molecular dynamics simulation of nanoscale convective heat transfer with the effect of axial heat conduction

Effective heat dissipation from nano-fluidic devices is sometimes necessary to ensure their performance and lifespan. In the molecular dynamics simulation of nanoscale convective heat transfer, thermostats cannot be directly applied to the fluid because of the non-uniform temperature distribution. Periodic boundary is typically utilised, but unrealistic axial heat conduction exists when there is a temperature difference between the outlet and images of inlet atoms. In this paper, the effect of axial conduction caused by periodic boundary is investigated through the Péclet number (Pe). Taking viscous dissipation into consideration, the magnitude of outlet thermal diffusion is observed to decrease with increasing Pe. The local average temperature of fluid changes in an exponential form except in the region close to the outlet. Results show that the contribution of outlet axial conduction to the local average temperature is less than 2.0% when Pe > 10. The main reason is that the magnitude of fluid velocity and viscous heat dissipation in nanochannels is much larger than that in macro-channels at the same Péclet number.     

Near-field heat transfer: A radiative interpretation of thermal conduction

It is shown in this article that the near-field radiative heat transfer can be interpreted as a conduction heat transfer due to the propagation of polaritons. We consider two situations. In the first one, two heated bodies at different temperatures are separated by a gap and in the second one a temperature gradient is imposed to a bulk material. In both situations, the radiative heat transfer is calculated by means of fluctuational electrodynamics. Asymptotic expressions of a thermal conductivity are obtained from the radiative heat transfer calculation. We interpret this conductivity as a consequence of the heat transfer by propagation and collisions of polaritons.     

Modified equations for heat conduction

It is shown that the form of the modifications previously suggested for the heat conduction equations when macroscopic parameters are changing rapidly may be incorrect when the heat carriers' relaxation time is wave number dependent. Even when the relaxation time is constant it is shown that for insulators the correction terms previously suggested are in error by a factor of 5.     

A thermodynamic approach to heat and electric conduction in solids

Heat and electric conduction in a rigid solid is investigated in the framework of extended irreversible thermodynamics. This allows us to apply directly the original procedure of Onsager to the analysis of the reciprocal relations. A non-local constitutive equation for the heat flux previously obtained is compared with microscopic equations used for the analysis of second sound in solids. A hydrodynamical analogy of this equation leads to the possibility of a turbulent phonon flow under some specific physical conditions.